PRECALCULUS ALGEBRA MAC 1140
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This 7 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1140 at University of Florida taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/207050/mac-1140-university-of-florida in Calculus and Pre Calculus at University of Florida.
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Date Created: 09/19/15
REVIEW UNIT 1 MAC 1140 L1L6 FORMULAS TO MEMORIZE x if x Z 0 lxl lxl Z 0 x 1f x lt 0 xy2 x22xyy2 xy2xz2xyy2 xZy2xyxy xSy3xyx2xyy2 x3y3xyx2xyy2 xy3 x3 3x2y3xy2 y3 xy3x33x2y3xy2y3 lx 2x lib2 4ac The Quadratic Formula x 2 a Equation of a circle with radius r and center h k x h2 y k2 r2 Distance on the plane between points x1 y1 and x2y2 d x2 x12 y2 y1 2 Midpoint Formula M The slope ofthe line through xly1 and x2y2 m E H Ax x2 x1 Equation of the line with slope m through the point x1y1 y y1 mx q Equation ofthe line with x and y intercepts a and b l a 7i 0 b at 0 a fxZfxi x1 Average rate of change of f from x1 to 62 is 62 x1 1 Write without absolute value signs and simplify 2x l x2 1 3 x 1 2 Find the real zeros of the functions a x4 l b xl2 16 c 2x2 x 5 d fx x2 3x3 3 What must be the value of k for the equation 6x2 3x k 0 to have one repeated real solution b l7r 5l 3 7239 c 3lZ 4rr ll ifrgt3 4 Solve the quadratic equation by completing the square 4x2 4x 35 0 5 Solve the absolute value inequalities Give answers in interval notation a 2l2 xISO b 2l2 xIZO 8 2x 3 1 1 C 4 TE gt0 3 xllt3 6 Write the statement below as absolute value inequality and solve it for k Give your answer in interval notation k is no more than 13 units away from 5 7 Given points P 35 and Q3 2 a Find dP b Find the midpoint of the segment joining the two points c Determine whether the point 69 79 is on the line passing through the points P and 8 If 37 is the endpoint ofa line segment and 4 8 is its midpoint find the other endpoint 9 What types of symmetry does the graph of 3x2 5y2 16 have if any 10 Marty s Tee Shirt amp Jacket Company is to produce a new line ofjackets with a embroidery of a Great Pyrenees dog on the front There are fixed costs of 570 to set up for production and variable costs of 37 per jacket Write an equation that can be used to determine the total cost CX encountered by Marty s Company in producing X jackets and use the equation to find the total cost of producing 94 jackets 11 Find the domain of each function For the functions in a and b find the range a fx 4 b fxx44 c mung 12 Find the equation ofthe circle with center 5 3 passing through the point 1 0 13 Find the centerradius equation of a circle if the endpoints of the diameter are l 2 and 9 6 14 Complete the square to find center and radius of the circle 3x2 3y2 12x 6y l 0 15 39 L 39 39 39 7673 throu 71 2 and 74 Give the nal answer in a standardforrn 16 Write the equation ofthe line through the point 3 2 perpendicular to the line 3 2 y 6 Give the nal answer in the slopeintercept form What is the y rintercept h s 17 1f fx 4x2 73x 2 find and simplify the difference quotient h a 0 18 A piecewise de ned function is given 7673 if for 71 if 72ltxlt1 x21 if 1621 Fimt f 2 f 0 f 1 19 Which ofthe followingrelations define y as a function of x a xrly35 by2723x cy lx29 d y374x710 20 classify the following functions as even odd or neither even nor odd 2 a x a3 a 2 b N 21 Findthe averagerate ofchange of fgtc I ontheinterval 7371 6 22 The graph ofa piecewisede ned function is given a Give the domain of the function h Find the range 39 39 tit 19min u an r1 constant d Find the relative maxima and niininia if any e Give the interval 5 on which fa g 0 REVIEW UNIT II MAC1140 FORMULAS TO MEMORIZE l quot aquot aifnis evenn22 Val quot61 ifnis oddnZ3 2 a7 quot am 5 provided 2 exists 3 Rules for the Inverses a f 1 x for all x in the domain off ff 1 y for all x in the domain off equivalently fxy G f391yx b Domain of f 1 Range of f Range of f 391 Domain of f c The graphs of f and f 391 are re ections of each other across the line y x 4 Variations Direct y kx Inverse y E Joint z kxy x 5 The vertex ofthe parabola ax2 bx C is h k where h b and kfh 2a A 6 For a linear function fx mx b the average rate of change E m l Simplify Assume that all variables are positive When they appear Rationalize the denominator Where it is necessary 4x10y12 x2 xy 2 2 2 a 5 b c d 3 x 4 x 164x523y 0 54 Nixg J yd y 2 Simplify each radical expression Where it is possible a 16x2 b JE 5 c l6x l62 x 34x 4 d lazb2 3 Evaluate 1 81 i 1 0 2 a 9 16 2 b 256 4 Solve the equations a aw b lxz10xll3x c mix51 d xl73xl7100 x UZ IJHI a Find the domain of the function f b Simplify the expression for c Rewrite f x as a piecewise defined function d Graph the function 5 Given 1 6 The graph of a piecewise defined function is given Find an equation of the function 7 Sketch the graph of the piecewise defined function 7x if x lt 72 fx 2 if 72 x 0 x7371 if xgt o a Give the largest open intervals on which the function is increasing decreasing or constant c Find all Xintercepm and yintercept if any h Give the intervals on which fx S 0 8 Let fx xl gx 2x and hx Find the following 2 a f 0 g b 9714 c Ffoh and its domain d Graph the function F x 9 Find 1 such that the range ofthe function 7x2 bx is 700 9 10 Find the equation of the quadratic function whose graph has vertex at 1 2 and an xintercept x 3 Find another xintercept of the parabola if any 11 List the transformations that could be applied to the graph of f x J in order to obtain the graph of gx 34 x 2 12 Analyze and graph the function f x 3x2 6x 5 a Give the vertex axis xintercepts yintercept domain and range b Graph the parabola 13 The height 3 of an object after t seconds is given by s l6t2 128t 50 Find the maximum height of the object and the time it takes the object to reach this height 14 Determine whether the functions fx lx l and g x x2 l x S 0 are the inverses of each other Explain 15 Determine whether the function defined by the table below is or linear fx mx b or nonlinear If the find the slope m and yintercept b 16 In the same coordinate system graph both functions fx x 22 l x Z 2 as a solid line and its inverse as a dashed line 17 While traveling at a constant speed in a car the centrifugal acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn If the passengers feel an acceleration of 12 feet per second per second ftsec 2 when the radius of the turn is 100 feet find the acceleration the passengers feel when the radius of the turn is 400 feet 18 A marina owner wishes to estimate a linear function that relates boat length in feet and its draft depth of boat below water line in feet He collects the following data Let boat length represent the independent variable and draft represent the dependent variable Use a graphing utility to draw a scatter diagram and to find the line of best fit What is the draft for a boat 60 ft in length to the nearest tenth Boat Length ft Draft ft 25 25 25 2 30 3 30 35 45 6 45 7 50 7 50 8 i z 19 Name two functions f and g such that o gx 5x2 3x4 20 Let fx i2 and gx ll x Find x a f gx and their domains g b 34 c fog0 d 0 gx g o fx and their domains 21 Which ofthe following functions f g and h are onetoone Ix 5 1 2 h gm x x x H 22 If fx is onetoone nd f 1 x and its domain and range afxx b fxx2 2x x21 c fxx22x x20 x d fx 2x 1l 4